Number of Elements in a Cartesian Product

Q. Let $A=\{1,4,7,10,13,16,19\},$ $B=\{1,2,3,4,5,6\},$ $C=\{2,8,14,20\},$ then $n[A\times (B^{\prime }\cap C^{\prime }{)}^{\prime }]=$

Q.

The Factorization of $12x+36$ is

Q. If $R$ is relation from $A$ to $B$, where $R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$, then the least value of $n(A\times B)$ is

1. $25$
2. infinite
3. $16$
4. $9$

Q. Let $A=\{x:(x-1\left)\right(x^2-10+21)=0\}$ and $B=\{y:y\text{is a prime factor of}42\}$, then the number of common elements between $A\times B$ and $B\times A$ is

Q. If $A=\{1,2,3\},B=\{4,5,6,7,8\},$ $C=\{4,8,12,16,20\},$ then $n\left[\right(A\times B)\cup (A\times C\left)\right]=$

1. $16$
2. $24$
3. $30$
4. $12$

Q. Given two sets $A=\{a,b,c,d\},B=\{b,c,d,e\}$, then $n\left[\right(A\times B)\cap (B\times A\left)\right]$ is

1. $3$
2. $16$
3. $4$
4. $9$

Q. If $A=\{3,6,9,12\},B=\{2,4,6,8,10\}$ and $C=\{4,8\},$ then $n\left(\right(A\times B)\cup (A\times C\left)\right)$ is

Q.

Given two finite sets A and B such that n(A) = 3, n(B) = 3. Then total number of relations from A to B is _____.

1. 4

2. 8

3. 512

4. 6

Q. If $A=\{3,5\}$ and $A\times B=B\times A$, then the correct option(s) can be

1. $B=\{x:x^2-8x+15=0\}$
2. $B=\{x:|x-4|=1\}$
3. $B=\{x:x\text{is prime factor of}15\}$
4. $B=\{x:x\in N,3\le x\le 5\}$

Q. If $A=\{a,b,2,3\},B=\{a,3,c\},$ $C=\{1,3,c\},$ then $n\left(\right(A\times B)\cap (A\times C\left)\right)$ is

1. $9$
2. $12$
3. $8$
4. $6$

Q. If $A=\{a,b,2,3\},B=\{a,3,c\},$ $C=\{1,3,c\},$ then $n\left(\right(A\times B)\cap (A\times C\left)\right)$ is

1. $9$
2. $12$
3. $6$
4. $8$

Q. If $n\left(A\right)=5,n\left(B\right)=7$ be two sets having $3$ elements in common then $n\left(\right(A\times B)\cap (B\times A\left)\right)=$

Q. If $A=\{5,6,7\},B=\{1,2,3,4\}$, then number of elements in set $(A-B)\times B$ is

1. $24$
2. $36$
3. $12$
4. $16$

Q. Let $A=\{1,3,5,7,9,11\},$ $B=\{3,9,27,81,243\},$ then $n\left[\right(A\times B)\cap (B\times A\left)\right]$ is

Q. Consider three sets $A,B,C$ such that set A contains all three digit numbers that are multiples of $4,$ set $B$ contains all three digit even numbers that are multiples of $3$ and set $C$ contains all three digit numbers that are multiples of $5.$ Then the value of $\frac{n\left[\right(A\cap B)\times (A\cap C\left)\right]}{n\left[\right(B\cap C)\times (A\cap B\cap C\left)\right]}$ is

1. $\frac{15}{2}$
2. $\frac{15}{4}$
3. $15$
4. $30$

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Then the number of elements in A $\times$ B is ___

Q.

If set A has p element and set B has q elements, then the number of element in set (A $\times$ B) is _____.

1. $\frac{P}{q}$

2. $p^q$

3. $p\times q$

4. $q^p$

Q. Let $A=\{a,b,c,d\},$ $B=\{b,c,e,f\},$ then $n\left(\right(A-B)\times (B-A\left)\right)=$

1. $4$
2. $16$
3. $8$
4. $12$

Q. If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to each of set $A\times B$ and $B\times A$ are

1. $2^{99}$
2. ${99}^2$
3. $100$
4. $18$

Q. If $A=\{3,5\}$ and $A\times B=B\times A$, then the correct option(s) can be

1. $B=\{x:x^2-8x+15=0\}$
2. $B=\{x:|x-4|=1\}$
3. $B=\{x:x\text{is prime factor of}15\}$
4. $B=\{x:x\in N,3\le x\le 5\}$

Q. Let $A\&B$ be two sets containing four and two elements respectively such that $A\cap B=\varphi$. Then the number of subsets of set $A\times B$ each having at least five elements is

Q. Let $A=\{1,2,3,4\},$ $B=\{4,5,6,7\},$ $C=\{3,6,9,12\}$ and $D=\{4,8,12,16,20\},$ then $n\left[\right(A\times B)\cap (C\times D\left)\right]$ =

1. $1$
2. $2$
3. $4$
4. $8$

Q. If $A=\{y:y={\log }_2|x-2|,x<5,x\text{is a whole number}\},B=\{y:y=|x-2|,x\in [0,1],y\in N\},C=\{1,3,5\}$
, then $n\left(\right(A\times B)\cap (B\times C\left)\right)$ is

1. $0$
2. $5$
3. $1$
4. $6$

Q.

A $\times$ A $\times$ A has 512 elements. Find the number of elements in A.

Q. Consider three sets $A,B,C$ such that set A contains all three digit numbers that are multiples of $4,$ set $B$ contains all three digit even numbers that are multiples of $3$ and set $C$ contains all three digit numbers that are multiples of $5.$ Then the value of $\frac{n\left[\right(A\cap B)\times (A\cap C\left)\right]}{n\left[\right(B\cap C)\times (A\cap B\cap C\left)\right]}$ is

1. $\frac{15}{2}$
2. $\frac{15}{4}$
3. $15$
4. $30$

Q. For any two sets $A\&B;n\left(A\right)=4,n\left(B\right)=7,n\left(A\Delta B\right)=3$, then, $n(A\cap B)=$

Q. If $R$ is relation from $A$ to $B$, where $R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$, then the least value of $n(A\times B)$ is

1. $25$
2. infinite
3. $16$
4. $9$

Q. Let $A=\{1,2,3,4,5\},$ $B=\{4,5,6,7,8\}$ and $C=\{8,9,10,11,12\},$ then $n[A\times (B^{\prime }\cup C^{\prime }{)}^{\prime }]=$